Speaking of all but touch, you get a love story. Jim Sturgess lives on one planet, Kirsten Dunst on the other. It’s like “West Side Story,” only with astronomy: two planets, one heart.

You get a dystopian fantasy. Sturgess’s planet, which everyone refers to as Down Below, is shot in grayish-blue and has the postwar look of a place that’s been through bad times, with much worse to come.

Finally, you get political allegory. Dunst’s planet, which everyone refers to as Up Above, exploits Down Below for minerals and other resources. It’s like a colony. When people want to ascend to Up Above, they have to pass through strict border controls. The controls are run by Transworld, a sinister multinational — make that multiplanetary. Even if you’re not from Latin America (writer-director Juan Solanas is Argentine), it’s hard to miss the commentary the movie offers on the state of immigration today. There’s also more than a whiff of miscegenation in Sturgess and Dunst’s romance.

UPSIDE DOWN

★★★

MPAA rating:

PG-13

MPAA rating reasons:

violence, emotional distress

Running time:

108 minutes

Cast:

Jim Sturgess, Kirsten Dunst, Timothy Spall

Director:

Juan Solanas

Writers:

Juan Solanas

Playing at:

Kendall Square

That quadripartite description might indicate the tonal difficulties “Upside Down” suffers from. Sometimes it’s very grim, sometimes very sweet, a few times very funny. There’s a sublime joke involving urine (that’s not a typo). The movie never quite comes together, but there’s so much going on that that’s not too much of a problem.

There’s so much going on because of how daring Solanas is. That daring can take the form of shamelessness. Sturgess’s character is named Adam, and Dunst’s Eden. Both amnesia and a fainting female figure in the plot. “Upside Down,’’ as noted, takes place in a different world — or worlds. It also appears to take place in a different century, though otherwise it very much resembles life as we know it on Earth (only without plasma-screen TVs).

More often, Solanas’s daring takes the form of ambition. “Upside Down” has a visionary look that has affinities with everything from “Metropolis” to “Blade Runner” to “Children of Men.” Solanas has the temerity to split the screen horizontally in many shots. Usually, this works, though “Upside Down” is not recommended for anyone subject to visual dislocation.

For example, we see Adam upright as he toils in his cubicle in a vast workplace Down Below; and we see overhead and inverted a helpful colleague named Bob (Timothy Spall), in his own cubicle in the Up Above level of that workplace (it’s an amazing space — and even more amazing seen mirrored and inverted). The planets, you will recall, are so close that they almost touch at certain points. So people can, under the right circumstances, hand items to each other. They’re that close.

Or they can reach out and make physical contact, which is how Adam (downtown boy) and Eden (uptown girl) first meet and fall in love. Up Above authorities interrupt one of their encounters, and the couple separate for 10 years. Then Adam sees Eden on television (the broadcasts all originate Up Above — one more sign of its quasi-imperial dominance). He resolves to get up there somehow and find her. “What if love is stronger than gravity?” Adam wonders in a voice-over at the beginning of “Upside Down.” It’s a rhetorical question.

Sturgess turns 35 in May. The puppy-boyishness he abounds in must be nearing its sell-by date. That said, he’s very appealing as Adam. As Eden, Dunst is pretty much restricted to looking winsome. She’s good at that, but you can feel her relief when she has a scene dancing a tango (remember, Solanas is Argentine). In a movie where falling head over heels assumes a whole new meaning, Dunst gets to kick up her heels, too.